60.2.1 problem Problem 1

Internal problem ID [15181]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 1
Date solved : Thursday, October 02, 2025 at 10:06:55 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+10 y&=100 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=10 \\ y^{\prime }\left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+10*y(x) = 100; 
ic:=[y(0) = 10, D(y)(0) = 5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 5 \,{\mathrm e}^{3 x} \sin \left (x \right )+10 \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 17

ode=D[y[x],{x,2}]-6*D[y[x],x]+10*y[x]==100; 
ic={y[0]==10,Derivative[1][y][0] ==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 5 \left (e^{3 x} \sin (x)+2\right ) \end{align*}

✓ Sympy. Time used: 0.120 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(10*y(x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 100,0) 
ics = {y(0): 10, Subs(Derivative(y(x), x), x, 0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 5 e^{3 x} \sin {\left (x \right )} + 10 \]